A new version of the multireference averaged coupled‐pair functional (MR‐ACPF‐2)

Abstract

ABSTRACT:The averaged coupled-pair functional (ACPF), as found in R. J. Gdanitz and R. Ahlrichs, Chem. Phys. Lett. 143 (1988), is probably the most successful method to approximate full configuration interaction (CI) on the multireference (MR) level of theory. However, ACPF has a tendency to slightly overestimate the effect of higher than double substitutions, which, when the zeroth-order wavefunction is of poor quality, may deteriorate the accuracy or even create instabilities. Since the properties of the ACPF and similar methods have apparently not always been correctly described in the literature, we repeat the derivation of this method in some detail. We analyze the connection between the (original) ACPF and the similar averaged quadratic coupled cluster (AQCC) method (which may be regarded as a damped ACPF), on one hand, and the different versions (0-3) of the coupled electron-pair approximation (CEPA), on the other hand. We find that ACPF and AQCC may be regarded as CEPA-1, respectively, CEPA-3, where the shifts of the Hamiltonian are substituted by a single averaged shift. As CEPA-3 considerably underestimates correlation effects, AQCC shows the same behavior. However, when the zeroth-order wavefunction is of poor quality, AQCC may be more stable and thus more accurate than ACPF. By analyzing the role of the single substitutions, we find that ACPF may especially overestimate their contribution to unlinked clusters like 1 2T 2 1 . We therefore propose a new version, called ACPF-2, where (in contrast to AQCC) only the renormalization factor, g, that corresponds to the singles, is damped; i.e., we have (4/N)[1 − 1/(2N − 2)]. In the limit of a large number of electrons, N, this factor becomes two times as large as in the (original) ACPF, where 2/N is used. In order to test the new ACPF-2 method, we perform numerous comparisons with full CI, as well as calculations including terms that are linear in the interelectronic distances, r ij . We find that in difficult cases, ACPF-2 is of similar stability as is AQCC and is thus considerably more accurate GDANITZ than the original ACPF. In contrast to AQCC, however, ACPF-2 achieves this stability without sacrificing the high accuracy which is obtained by ACPF in well-behaved cases.

Progress and Challenges in the Calculation of Electronic Excited States

“…[58] Another size-extensive modification of singles and doubles MRCI is the averaged coupled pair functional (ACPF) theory. [59][60][61] The combination of the MRCI method with the recently developed Cholesky decomposition technique to reduce the cost of the handling of the two-electron integrals is expected to increase the range of applicability of this methodology. Efforts to reduce the cubic-to-quartic scaling of singles and doubles MRCI to linear scaling using local correlation and integral screening have been presented recently.…”

Ab Initio Ground‐State Potential Energy Function and Vibration‐Rotation Energy Levels of Aluminum Monohydride

“…The vibration-rotation energy levels of AIH were calculated using the Numerov-Cooley method. [34] The energy levels were calculated using the nuclear masses of aluminum and hydrogen (26.974406991, 1.007276452, and 2.013553198 u for 27 Al, H, and D, respectively).…”

Density matrix renormalization group for ab initio Calculations and associated dynamic correlation methods: A review of theory and applications

“…[169] As a result of addressing these challenges, we presented that the DMRG-MRCI is free from the exponential bottleneck and its scalability is polynomial order versus the number of orbitals including active orbitals. The approach was extended to the size-consistencycorrected variants of MRCI, such as the MRCI1Q, [104,[170][171][172][173] MR-ACPF, [105,174,175] and MR-AQCC [106,176,177] methods.…”